Simplify. \[ \left(-3 x y z^{3}\right)\left(-x^{2} y^{3} z^{4}\right)^{2} \] \( \square \)

To simplify the expression \(\left(-3 x y z^{3}\right)\left(-x^{2} y^{3} z^{4}\right)^{2}\), we first deal with the exponent in the second term. Calculating \(\left(-x^{2} y^{3} z^{4}\right)^{2}\) gives us: \[ (-1)^{2}(x^{2})^{2}(y^{3})^{2}(z^{4})^{2} = 1 \cdot x^{4} \cdot y^{6} \cdot z^{8} = x^{4} y^{6} z^{8} \] Now, we can rewrite the entire expression: \[ \left(-3 x y z^{3}\right)(x^{4} y^{6} z^{8}) \] Next, we multiply the coefficients and add the exponents of like bases: 1. Coefficient: \(-3 \times 1 = -3\) 2. For \(x\): \(x^{1} \cdot x^{4} = x^{1 + 4} = x^{5}\) 3. For \(y\): \(y^{1} \cdot y^{6} = y^{1 + 6} = y^{7}\) 4. For \(z\): \(z^{3} \cdot z^{8} = z^{3 + 8} = z^{11}\) Putting it all together, we have: \[ -3 x^{5} y^{7} z^{11} \] Thus, the simplified expression is: \[ \boxed{-3 x^{5} y^{7} z^{11}} \]